One can also have situations where someone knows more than everything. This is known as quantum ‘entanglement’, and when two people share entanglement, there can be negative information.
I'm pretty sure I've seen this situation, even without quantum particles.
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At risk of disturbing the concept of negative information, I note that it is common in physics to extend definitions. The concept of imaginary temperature is very useful, for example...
And science reporting is generally awful ...
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